The notion of degeneration is extensively applied in moduli problems and curve counting theories in enumerative geometry. Good degenerations are introduced by Jun Li [[1]}] as an appropriate class of degenerations to investigate the geometry of moduli spaces, and their constructions depend on the notion of the stack of expanded degenerations. In [[2]}], the author constructs the good degeneration of moduli of stable morphisms to a simple degeneration of projective varieties, which leads to a degeneration formula of Gromov-Witten (GW) invariants [[3]}]. With the construction of good degenerations of Grothendieck's Quot schemes (including Hilbert schemes of curves) and of moduli of coherent systems (or Pandharipande-Thomas (PT) stable pairs) on any simple degeneration [[4]}], the authors derive degeneration formulas of Donaldson-Thomas (DT) invariants and of PT invariants (see also [[5]}]) for projective 3-folds. Degeneration formulas of the above three curve counting theories are not only useful for computing their invariants and even determining their structures (e.g., [[6]}, [7]}, [8]}]), but also important for proving GW/DT and GW/PT correspondence [[6]}, [7]}, [11]}, [5]}].
